Projectile is a body thrown with an
initial velocity in the vertical plane and then it
moves in two dimensions under the action of gravity
alone without being propelled by any engine or
fuel.Its motion is called projectile motion.The path
of a projectile is called its trajectory.

Examples:

A packet released from an
airplane in flight.

A golf ball in flight.

A bullet fired from a rifle.

A jet of water from a hole
near the bottom of a water tank.

Projectile motion is a case of
two-dimensional motion .Any case of two dimensional
motion can be resolved into two cases of one
dimensional motion -one along the x-axis and the
other along the y-axis.The two cases can be studied
separately as two cases of one dimensional motion.The
results from two cases can be combined using vector
algebra to see the net result

What is important to remember is that
the motion along the horinzontal direction does not
affect the motion along the vertical direcion and
vice versa.Horizontal motion and vertical motion are
totally independent of each other .

A body can be projected in two ways :

Horizontal projection-When
the body is given an initial velocity in the
horizontal direction only.

Angular projection-When the
body is thrown with an initial velocity at an
angle to the horizontal direction.

We will study the two cases
separately.We will neglect the effect of air
resistance.We will take x-axis along the horizontal
direction and y-axis along the vertical direction.

We
will now consider the case when the object is
projected with an initial velocity u at an angle to
the horizontal direction.

We
assume that there is no air resistance .Also since
the body first goes up and then comes down after
reaching the highest point , we will use the
Cartesian convention for signs of different physical
quantities.The acceleration due to gravity 'g'
will be negative as it acts downwards.

We
will separate the motion into horizontal motion
(motion along x-axis) and vertical motion (motion
along y-axis) .We will study x-motion and y-motion
separately.

X axis

Y axis

1. Component of initial velocity along
x-axis.ux=u
cosΦ

1. Component of initial velocity along
y-axis.uy=u
sinΦ

2.
Acceleration along x-axisax=0(Because no
force is acting along the horizontal
direction)

2.Acceleration
along y-axisay=
-g= -9.8m/s2(g
is negative as it is acting in the downward
direction)